This paper addresses the material dispersion effects on the propagation characteristics of an omega nonradiative dielectric (NRD) waveguide. The omega NRD waveguide is an H-guide, working in the closed-waveguide regime, where the common isotropic slab is replaced by an omega slab. For the first time, a single-resonance lossless model is used for the material constitutive parameters of the omega NRD waveguide. The dispersion diagrams reflect the dispersive characteristics of the medium. In addition to the surface guided modes, proper leaky modes are found to propagate in the frequency range above the resonance, where some of the constitutive parameters become negative.